How to animate a kite tail?
Cloth Simulation
Simple Cloth simulation seems to work quite well with Wind effector.
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Just play anim and move (G) the Empty arround.
It can be used as a proxy mesh for more detailed model with Surface Deform Modifier.


Spring Bone add-on
just a quick test ... it has gravity parametr, but they can't be influence by effectors like wind.
Download add-on from Github


Add-on in included in blend file too.